DUKE MATHEMATICIAN TO DESCRIBE HOPES FOR STRING THEORY

PHILADELPHIA -- Duke University mathematician David Morrison says
he is applying his expertise in algebraic geometry to the exotic field of
string theory in a quest for simplicity.

"It is kind of a philosophical question," the James B. Duke professor of
mathematics and physics said in an interview. "Do we expect the laws of
nature to be based on simple mathematical principles that we can
understand and then derive other things from?"

Morrison planned to discuss how string theory modifies the world around
us in a talk Monday entitled "The Small-Scale Structure of Spacetime"
during the American Association for the Advancement of Science's 1998
annual meeting.

String theory posits that each type of elementary subatomic particle is a
kind of vibrating geometric entity that mathematically resembles a string.

One of those vibrational modes corresponds to gravity. Others correspond
to the additional forces in nature, including electromagnetism, as
manifested in light rays and radio waves. Still other modes include the
basic elementary particles out of which matter is built.

These strings would also be infinitesimally tiny, each as small in relation
to a subatomic proton as a proton is small in relation to the entire solar
system.

The catch in the promising theory, however, was that it requires these
entities to vibrate in 10 dimensions rather than the four that humans live
in -- three spatial and one time dimension. Somehow, those six additional
dimensions must be made to fold into spaces too tiny to be apparent to
humans.

In the recent interview, Morrison described how string theory evolved in
an attempt to reconcile mathematical incompatibilities between two of
physics' most highly successful theories: quantum mechanics and the
general theory of relativity.

Quantum mechanics describes the nature and behavior of a multitude of
different elementary particles envisioned as the building blocks of our
physical universe. And the general theory of relativity describes the
nature of gravity and its geometric relationship with space and time.

Despite their sometimes counterintuitive natures, both theories have been
consistently borne out by scientific experiments. And since both matter
and light are affected by the force of gravity, one theory logically should
be consistent with the other.

"We don't understand how they can be made to interact in a consistent
fashion," Morrison said of both theories. "The only concrete proposal that
we have for doing that -- at the moment -- is string theory, which is why
many of us are excited about it."

The problem has been that attempts to reconcile the two theories result
in mathematical inconsistencies at the extremely small scales at which
quantum mechanics operate. Fluctuations which are an integral part of
quantum mechanics require that the geometry of time and space be torn
asunder, which violates a fundamental rule of general relativity, he said.

Another motivation for string theory, Morrison said, is that "there is
something quite dissatisfying about the current Standard Model of particle
physics." That's the quantum mechanics-based set of rules describing
how all those elementary particles interact.

The Standard Model uses equations "whose forms are rather complicated
and whose origins are not understood," he added. "It doesn't sound like a
fundamental theory. It doesn't sit right with a lot of people that such
should be the way that fundamental equations of the world work at the
smallest level."

String theorists have been seeking to overcome these drawbacks of
current theories by modifying both quantum mechanics and Albert
Einstein's relativity theory. The latter drew on the earlier geometric
insights of 19th century mathematician Georg Reimann to show how
gravity causes space and time to curve.

Mathematicians Theodr Kaluza and Oscar Klein showed, beginning in the
1920s, that Reimann's geometry could indeed be extended in a way that
allowed for tiny extra dimensions. And they showed that, when this is
done, other physical forces are included along with gravity.

Modern string theorists use a variant of that idea to attempt to address the
multidimensional problem in string theory. But another obstacle, Morrison
said, is that these "superstring" equations can be solved in tens of
thousands of different ways.

In 1995, Morrison joined physicists Brian Greene of Cornell University and
Andrew Strominger of the University of California at Santa Barbara to deal
with both those barriers.

They drew on work over the last two decades by mathematicians,
including Eugenio Calabi of the University of Pennsylvania and
Shing-Tung Yau of Harvard University, who discovered so-called
"Calabi-Yau manifolds." Those manifolds are six-dimensional
mathematical shapes, Morrison said, that can meet the "stringent
requirements"of string theory.

Mathematicians have found that, by employing algebraic geometry, these
Calabi-Yau manifolds "can be described by some rather simple looking
types of equations, the simplest kinds of equations we know how to
manipulate," he added.

Greene, Morrison and Strominger showed that certain geometrical
features of these manifolds would resemble special kinds of
submicroscopic "black holes" in our four-dimensional world. But as the
manifolds' shapes change, these black holes would have the capacity to
tear space-time in a way the relativity theory doesn't allow.

Just before that could happen, though, the investigators also found these
black holes could undergo a "phase change" similar to ice freezing into
water. After that shift, each type of the special black holes would be
transformed into a string, which would appear to us like a corresponding
type of elementary particle.

Morrison said this shift in the black hole's phase would be as dramatic as
cutting a hole in a drum to change the way it vibrates. Yet the rules of
quantum mechanics would permit it to happen, just like they allow
electrons to "tunnel" through a forbidden region, or permit the nuclei of
some atoms to decay.

"Similarly, a process like moving from one shape to a radically different
shape is something that's possible quantum-mechanically," he said. As a
bonus, Morrison, Greene and Strominger found their mathematics allows
the many different solutions of string theory to be linked together by these
phase transitions.

And what about all those extra dimensions that string theory also requires
to exist? "It's the folded up structure of that space which gives us
interesting clues about the small-scale structure of space time," he said.

Morrison stressed that string theory is still unproven, and could be
replaced by something else. "You can have beautiful theories which are
wrong -- not wrong as mathematics but as interpretations of the physical
world," he said.

But he also noted that Isaac Newton invented calculus to successfully
explain his theory of how gravity governs the motions of planets, and
Einstein later used more advanced forms of mathematics to reveal
something deeper about gravity.

"I think a number of people are still hoping for an analogous formulation
for the most fundamental of theories that would explain elementary
particles," he said. "And that's one of the motivations, certainly, that
drives the formulation of string theory."